The mean price for a 2,000sq foot home in FL is $240,000 with a Standard Deviation of $16,000. The mean price of the same sized home in OH is $170,000 with a standard deviation of $12,000. Which state would a home priced at $200,000 be closer to the mean price, compared to the distribution of prices in the state? Find the z score for each state.

The z-score for a home priced at $200,000 in Florida is of -2.5.

The z-score for a home priced at $200,000 in Ohio is of 2.5.

The closeness to the mean is measured by the absolute z-score(disconsidering the signal, the lower the score, the closer to the mean). However, in this case, both z-scores have the same absolute value, so in both Florida and Ohio a home priced at $200,000 is equally close to the mean.

Step-by-step explanation:

Z-score:

In a set with mean and standard deviation , the z-score of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The mean price for a 2,000sq foot home in FL is $240,000 with a Standard Deviation of $16,000. Home of $200,000.

This means that . So

The z-score for a home priced at $200,000 in Florida is of -2.5.

The mean price of the same sized home in OH is $170,000 with a standard deviation of $12,000. Home of $200,000.

This means that . So

The z-score for a home priced at $200,000 in Ohio is of 2.5.

Which state would a home priced at $200,000 be closer to the mean price, compared to the distribution of prices in the state?

The closeness to the mean is measured by the absolute z-score(disconsidering the signal, the lower the score, the closer to the mean). However, in this case, both z-scores have the same absolute value, so in both Florida and Ohio a home priced at $200,000 is equally close to the mean.

1/6

step-by-step explanation:

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)